Integers 1,2,3.....n are written on a board. Two numbers m,k are removed and average of the remaining numbers is 17. What is maximum value of m+n??

Question

n>2 and 1<m<n and 1<k<n

Answer 1

Setting this number progression into excel gives the following:

As can be seen from the conditions the smallest sequence that gives your three numbers is n=4, with m=3 & k=2.

Since you want to start maximizing the average your m and k stay 3 & 2.

At the sequence of 32 integers the average goes over 17 which gives you values of n=32, m=16 & k = 2 to average 17.

At 35 integers the average goes over 17 which gives you values of n=35, m=3 & k = 33 to average over 17.

So the highest value of N that you can remove two integers and have an average of 17 is 34.

This gives you n=34, m=33 and k=18.

I do not of a formula that could give you the answer, I could write a computer algorithm to solve it,